The Cauchy problem for an infinite one-dimensional system of particles with nonlinear viscoelastic ties; main estimates for the solution of the discrete problem; interpolation of grid functions; existence, uniqueness, and smoothness theorems for the solution of the Cauchy problem for a partial differential equation that is the limit equation for a nonlinear viscoelastic system; estimates for differences between solutions of the Cauchy problem for the basic equation (4.17); the Cauchy problem for an equation in general form; the Cauchy problem for a second-order hyperbolic equation with small third-order viscous terms; solvability of the Cauchy problem; solvability of the Cauchy problem for a system of equations; solution behavior in the case of vanishing viscosity; acoustic approximation; asymptotics of a shock wave in a barotropic medium.
